Method and arrangement for transformation of signals from a frequency to a time domain

ABSTRACT

An IDCT, or Inverse Discrete Cosine Transform, method decimates a 2-D IDCT into two 1-D IDCT operations and then operates separately on the even and odd pixel input words. In a common processing step, selected input values are passed directly to output adders and subtractors, while others are multiplied by constant, scaled cosine values. In a pre-common processing step, the lowest-order odd input word is pre-multiplied by √2, and the odd input words are summed pairwise before processing in a common processing step. In a post-common processing step, intermediate values corresponding to the processed odd input words are multiplied by predetermined coefficients to form odd resultant values. After calculation of the even and odd resultant values, the high-order and low-order outputs are formed by simple subtraction/addition, respectively, of the odd resultant values from/with the even resultant values. The input values are preferably scaled upward by a factor of √2. Selected bits of some intermediate resulting data words are optionally adjusted by forcing these bits to either &#34;1&#34; or &#34;0&#34;. The IDCT system includes a pre-common processing circuit (PREC), a common processing circuit (CBLK), and a post-common processing circuit (POSTC), which perform the necessary operations in the respective steps. The system also includes a controller (CNTL) to generate signals to control the loading of system latches and, preferably, to time-multiplex the application of the even and odd input words to latches in the pre-common circuit.

This invention relates to a method for the transformation of signalsfrom a frequency to a time representation, as well as a digital circuitarrangement for implementing the transformation.

It is a common goal in the area of telecommunications to increase bothinformation content and transmission speed. Each communications medium,however, imposes a limitation on transmission speed, as does thehardware at the transmitting and receiving end that must process thetransmitted signals. A telegraph wire is, for example, typically a muchfaster medium for transmitting information than the mail is, even thoughit might be faster to type and read a mailed document than to tap it outon a telegraph key.

The method of encoding transmitted information also limits the speed atwhich information can be conveyed. A long-winded telegraph message will,for example, take longer to convey than a succinct message with the sameinformation content. The greatest transmission and reception speed cantherefore be obtained by compressing the data to be transmitted as muchas possible, and then, using a high-speed transmission medium, toprocess the data at both ends as fast as possible, which often means thereduction or elimination of "bottlenecks" in the system.

One application in which it is essential to provide high-speedtransmission of large amounts of data is in the field of digitaltelevision. Whereas conventional television systems use analog radio andelectrical signals to control the luminance and color of pictureelements ("pixels") in lines displayed on a television screen, a digitaltelevision transmission system generates a digital representation of animage by converting analog signals into binary "numbers" correspondingto luminance and color values for the pixels. Modern digital encodingschemes and hardware structures typically enable much higher informationtransmission rates than do conventional analog transmission systems. Assuch, digital televisions are able to achieve much higher resolution andmuch more life-like images than their conventional analog counterparts.It is anticipated that digital television systems, including so-calledHigh-Definition TV (HDTV) systems, will replace conventional analogtelevision technology within the next decade in much of theindustrialized world. The conversion from analog to digital imaging, forboth transmission and storage, will thus be similar to the change-overfrom analog audio records to the now ubiquitous compact discs (CD's).

In order to increase the general usefulness of digital image technology,standardized schemes for encoding and decoding digital images have beenadopted. One such standardized scheme is known as the JPEG standard andis used for still pictures. For moving pictures, there are at presenttwo standards--MPEG and H.261--both of which carry out JPEG-likeprocedures on each of the sequential frames of the moving picture. Togain advantage over using JPEG repeatedly, MPEG and H.261 operate on thedifferences between subsequent frames, taking advantage of thewell-known fact that the difference, that is the movement, betweenframes is small; it thus typically takes less time or space to transmitor store the information corresponding to the changes rather than totransmit or store equivalent still-picture information as if each framein the sequence were completely unlike the frames closest to it in thesequence.

For convenience, all the current standards operate by breaking an imageor picture into tiles or blocks, each block consisting of a piece of thepicture eight pixels wide by eight pixels high. Each pixel is thenrepresented by three (or more) digital numbers known as "components" ofthat pixel. There are many different ways of breaking a colored pixelinto components, for example, using standard notation, YUV, YC_(r)C_(b), RGB, etc. All the conventional JPEG-like methods operate on eachcomponent separately.

It is well known that the eye is insensitive to high-frequencycomponents (or edges) in a picture. Information concerning the highestfrequencies can usually be omitted altogether without the human viewernoticing any significant reduction in image quality. In order to achievethis ability to reduce the information content in a picture byeliminating high-frequency information without the eye detecting anyloss of information, the 8-by-8 pixel block containing spatialinformation (for example the actual values for luminance) must betransformed in some manner to obtain frequency information. The JPEG,MPEG and H.261 standards all use the known Discrete Cosine Transform tooperate on the 8-by-8 spatial matrix to obtain an 8-by-8 frequencymatrix.

As described above, the input data represents a square area of thepicture. In transforming the input data into the frequencyrepresentation, the transform that is applied must be two-dimensional,but such two-dimensional transforms are difficult to computeefficiently. The known, two-dimensional Discrete Cosine Transform (DCT)and the associated Inverse DCT (IDCT), however, have the property ofbeing "separable". This means that rather than having to operate on all64 pixels in the eight-by-eight pixel block at one time, the block canfirst be transformed row-by-row into intermediate values, which are thentransformed column-by-column into the final transformed frequencyvalues.

A one-dimensional DCT of order N is mathematically equivalent tomultiplying two N-by-N matrices. In order to perform the necessarymatrix multiplication for an eight-by-eight pixel block, 512multiplications and 448 additions are required, so that 1,024multiplications and 896 additions are needed to perform the full2-dimensional DCT on the 8-by-8 pixel block. These arithmeticoperations, and especially multiplication, are complex and slow andtherefore limit the achievable transmission rate; they also requireconsiderable space on the silicon chip used to implement the DCT.

The DCT procedure can be rearranged to reduce the computation required.There are at present two main methods used for reducing the computationrequired for the DCT, both of which use "binary decimation." The term"binary decimation" means that an N-by-N transform can be computed byusing two N/2-by-N/2 transformations, plus some computational overheadwhilst arranging this. Whereas the eight-by-eight transform requires 512multiplications and 448 additions, a four-by-four transform requiresonly 64 multiplications and 48 additions. Binary decimation thus saves384 multiplications and 352 additions and the overhead incurred inperforming the decimation is typically insignificant compared to thisreduction in computation.

At present, the two main methods for binary decimation were developedByeong Gi Lee ("A New Algorithm to Compute the DCT", IEEE Transactionson Acoustics, Speech and Signal Processing, Vol. Assp 32, No. 6, p.1243, December 1984), and Wen-Hsiung Chen ("A Fast ComputationalAlgorithm for the DCT", Wen-Hsiung Chen, C. Harrison Smith, S.C.Pralick, IEEE Transactions on Communications, Vol. Com 25, No. 9, p.1004, September 1977.) Lee's method makes use of the symmetry inherentin the definition of the inverse DCT and by using simple cosineidentities it defines a method for recursive binary decimation. The Leeapproach is only suitable for the IDCT. The Chen method uses a recursivematrix identity that reduces the matrices into diagonals only. Thismethod provides easy binary decimation of the DCT using known identitiesfor diagonal matrices.

A serious disadvantage of the Lee and Chen methods is that they areunbalanced in respect of when multiplications and additions must beperformed. Essentially, both of these methods require that manyadditions be followed by many multiplications, or vice versa. Whenimplementing the Lee or Chen methods in hardware, it is thus notpossible to have parallel operation of adders and multipliers. Thisreduces their speed and efficiency, since the best utilization ofhardware is when all adders and multipliers are used all the time.

An additional disadvantage of such known methods and devices forperforming DCT and IDCT operations is that it is usually difficult tohandle the so-called normalization coefficient, and known architecturesrequire adding an extra multiplication at a time when all themultipliers are being used.

Certain known methods for applying the forward and inverse DCT to videodata are very simple and highly efficient for a software designer whoneed not be concerned with the layout of the semiconductor devices thatmust perform the calculations. Such methods, however, often are far tooslow or are far too much complex in semiconductor architecture andhardware interconnections to perform satisfactorily at the transmissionrate desired for digital video.

Yet another shortcoming of existing methods and hardware structures forperforming DCT and IDCT operations on video data is that they requirefloating-point internal representation of numerical values. Toillustrate this disadvantage, assume that one has a calculator that isonly able to deal with three-digit numbers, including digits to theright of the decimal point (if any). Assume further that the calculatoris to add the numbers 12.3 and 4.56. (Notice that the decimal point isnot fixed relative to the position of the digits in these two numbers.In other words, the decimal point is allowed to "float".) Since thecalculator is not able to store the four digits required to fullyrepresent the answer 16.86, the calculator must reduce the answer tothree digits either by truncating the answer by dropping the right-most"6", yielding an answer of 16.8, or it must have the necessary hardwareto round the answer up to the closest three-digit approximation 16.9.

As this very simple example illustrates, if floating-point arithmetic isassumed or required, one must either accept a loss of precision orinclude highly complicated and space-wasting circuitry to minimizerounding error. Even with efficient rounding circuitry, however, theaccumulation and propagation of rounding or truncation errors may leadto unacceptable distortion in the video signals. This problem is evengreater when the methods for processing the video signals requireseveral multiplications, since floating-point rounding and truncationerrors are typically even greater for multiplication than for addition.

A much more efficient DCT/IDCT method and hardware structure wouldensure that the numbers used in the method could be represented with afixed decimal point, but in such a way that the full dynamic range ofeach number could be used. In such a system, truncation and roundingerrors would either be eliminated or at least greatly reduced.

In the example above, if the hardware could handle four digits, nonumber greater than 99.99 were ever needed, and every number had thedecimal point between the second and third places, then the presence ofthe decimal point would not affect calculations at all, and thearithmetic could be carried out just as if every number were an integer:the answer 1230+0456=1686 would be just as clear as 12.30+4.56=16.86,since one would always know that the "1686" should have a decimal pointbetween the middle "6" and "8". Alternatively, if numbers (constant orotherwise) are selectively scaled or adjusted so that they all fallwithin the same range, each number in the range could also be accuratelyand unambiguously represented as a set of integers.

One way of reducing the number of multipliers needed is simply to have asingle multiplier that is able to accept input data from differentsources. In other words, certain architectures use a single multiplierto perform the multiplications required in different steps of the DCT orIDCT calculations. Although such "crossbar switching" may reduce thenumber of multipliers required, it means that large, complicatedmultiplexer structures must be included instead to select the inputs tothe multiplier, to isolate others from the multiplier, and to switch theappropriate signals from the selected sources to the inputs of themultiplier. Additional large-scale multiplexers are then also requiredto switch the large number of outputs from the shared multipliers to theappropriate subsequent circuitry. Crossbar switching or multiplexing istherefore complex, is generally slow (because of the extra storageneeded), and costs significant area in a final semiconductorimplementation.

Yet another drawback of existing architectures, including the "crossbarswitching", is that they require general purpose multipliers. In otherwords, existing systems require multipliers for which both inputs arevariable. As is well known, implementations of digital multiplierstypically include rows of adders and shifters such that, if the currentbit of a multiplier word is a "one", the value of the multiplicand isadded into the partial result, but not if the current bit is a "zero".Since a general purpose multiplier must be able to deal with the case inwhich every bit is a "1", a row of adders must be provided for every bitof the multiplier word.

By way of an example, assume that data words are 8 bits wide and thatone wishes to multiply single inputs by 5. An 8-bit representation ofthe number 5 is 00000101. In other words, digital multiplication by 5requires only that the input value be shifted to the left two places(corresponding to multiplication by 4) and then added to its un-shiftedvalue. The other six positions of the coefficient have bit values of"0", so they would not require any shifting or addition steps.

A fixed-coefficient multiplier, that is, in this case, a multipliercapable of multiplying only by five, would require only a single shifterand a single adder in order to perform the multiplication (disregardingcircuitry needed to handle carry bits). A general purpose multiplier, incontrast, would require shifters and adders for each of the eightpositions, even though six of them would never need to be used. As theexample illustrates, fixed coefficients can simplify the multiplierssince they allow the designer to eliminate rows of adders thatcorrespond to zeros in the coefficient, thus saving silicon area.

Various aspects of the invention are exemplified by the attached claims.

In a IDCT method according to a further aspect of the invention, aone-dimensional IDCT for each N-row and N-column of N-by-N pixel blocksis decimated and a 1-D IDCT is performed separately on the N/2even-numbered pixel input words and the N/2 odd-numbered pixel inputwords.

In a preferred embodiment, N=8 according to the JPEG standard. Thetwo-dimensional IDCT result is then obtained by performing twoone-dimensional IDCT operations in sequence (with an intermediatereordering--transposition--of data).

In a common processing step, for N=8, a first pair of input values ispassed without need for multiplication to output adders and subtractors.Each of a second pair of input values is multiplied by each of twoconstant-coefficient values corresponding to two scaled cosine values.No other multiplications and only one subtraction and one addition arerequired in the common processing step. The second pair is then added ordifferenced pairwise with the first pair of input values to form even orodd resultant values.

In a pre-common processing stage, the lowest-order odd input word ispre-multiplied by √2, and the odd input words are summed pairwise beforeprocessing in a common processing block. In a post-common processingstage, intermediate values corresponding to the processed odd inputwords are multiplied by predetermined constant coefficients to form oddresultant values.

After calculation of the even and odd resultant values, the N/2high-order outputs are formed by simple subtraction of the odd resultantvalues from the even resultant values, and the N/2 low-order outputs areformed by simple addition of the odd resultant values and the evenresultant values.

For both the DCT (at the transmission end of a video processing system)and the IDCT (at the receiving end, which incorporates one or more ofthe various aspects of the invention), the values are preferablydeliberately scaled upward by a factor of √2. After the DCT/IDCToperations are performed, the resulting values may then be scaleddownward by a factor of two by a simple binary right shift. Thisdeliberate, balanced, upward scaling eliminates several multiplicationsteps that are required according to conventional methods.

According to another aspect of the method, selected bits of constantcoefficients or intermediate resulting data words are rounded oradjusted by predetermined setting of selected bits to either "1" or "0".

Two-dimensional transformation of pixel data is carried out by a second,identical 1-D operation on the output values from the first 1-D IDCTprocessing steps.

An IDCT system according to yet another aspect of the invention includesa pre-common processing circuit, a common processing circuit, and apost-common processing circuit, in which the pre-common, common, andpost-common processing calculations are performed on input data words. Asupervisory controller generates control signals to control the loadingof various system latches; preferably, to serially time-multiplex theapplication of the N/2 even- and N/2 odd-numbered input words to inputlatches of the pre-common block; to direct addition of the even and oddresultant values to form and latch low-order output signals and todirect subtraction of the odd resultant values from the even resultantvalues to form and latch the high-order output signals; and tosequentially control internal multiplexers.

Even and odd input words are preferably processed in separate passesthrough the same processing blocks. Input data words are preferably (butnot necessarily) latched not in strictly ascending or descending order,but rather in an order enabling an efficient "butterfly" structure fordata paths.

At least the common processing circuit may be configured as a pure-logiccircuit, with no clock or control signals required for its properoperation, as may be other processing blocks depending on the particularapplication.

No general-purpose multipliers (with two variable inputs) are required;rather constant coefficient multipliers are included throughout thepreferred embodiment. Furthermore, fixed-point integer arithmeticdevices are included in the preferred embodiment for all requiredarithmetic operations.

It will be apparent that certain embodiments of the invention can be sodesigned as to provide a method and system for performing IDCTtransformation of video data with one or more of the following features:

(1) constant use of all costly arithmetic operations;

(2) in order to reduce the silicon area needed to implement the IDCT,there are a small number of storage elements (such as latches),preferably no more than required for efficient pipelining of thearchitecture, coupled with a small number of constant coefficientmultipliers rather than general purpose multipliers that require extrastorage elements;

(3) operations are arranged so that each arithmetic operation does notneed to use sophisticated designs; for example, if known "ripple adders"are used, these would sufficient time to "resolve" (see below) orproduce their answers; if operations are arranged in such a way thatother devices preceding such a ripple adder in the data path are to beheld idle while waiting for the adder to finish, then rearrangingoperations to avoid this delay should lead to greater throughput andefficiency;

(4) one is able to generate results in a natural order;

(5) no costly, complex, crossbar switching need be required;

(6) the architecture is able to support much faster operations; and

(7) the circuitry used to control the flow of data through the transformhardware can be small in area.

For a better understanding of the invention and to show how the same maybe carried into effect, reference will now be made, by way of example,to the accompanying drawings, in which:

FIG. 1 is a simplified illustration of basic steps in a method accordingto the invention for performing the IDCT on input data;

FIG. 2 is a block diagram that illustrates the combined, simplified,two-stage architecture of an IDCT system according to the invention;

FIG. 3 is a simplified block diagram of the integrated circuits thatcomprise the main components of the IDCT system;

FIG. 4a and 4b together are a block diagram of a pre-processing circuitcorresponding to one of the main system components; for ease ofexplanation, these figures are referred to collectively as FIG. 4;

FIGS. 5a and 5b together are a block diagram of a common processingcircuit in the IDCT system; for ease of explanation, these figures arereferred to collectively as FIG. 5;

FIGS. 6a, 6b, 6c, and 6d together are a block diagram of apost-processing circuit that corresponds to another main component ofthe system; except as necessary to emphasize certain features, thesefigures are referred to collectively as FIG. 6; and

FIGS. 7a, 7b, 7c are timing diagrams that show the relationships betweentiming and control signals in the IDCT system in the preferredembodiment.

THEORETICAL BACKGROUND OF THE INVENTION

In order to understand the purpose and function of the variouscomponents and the advantages of the signal processing method used inthe IDCT system according to the invention, it is helpful to understandthe system's theoretical basis.

Separability of a Two-Dimensional IDCT

The mathematical definition of a two-dimensional forward discrete cosinetransform (DCT) for an N×N block of pixels is as follows, where Y(j,k)are the pixel frequency values corresponding to the pixel absolutevalues X(m,n): ##EQU1## where j,k=0, 1, . . . , N-1 and ##EQU2##

The term 2/N governs the dc level of the transform, and the coefficientsc(j), c(k) are known as normalization factors.

The expression for the corresponding inverse discrete cosine transform,that is for the IDCT, is as follows: ##EQU3## wherein j,k=0, 1, . . . ,N-1 and ##EQU4##

The forward DCT is used to transform spatial values (whetherrepresenting characteristics such as luminance directly, or representingdifferences, such as in the MPEG standard) into their frequencyrepresentation. The inverse DCT, as its name implies, operates in theother "direction", that is the IDCT transforms the frequency values backinto spatial values.

In the expression E2, note that the cosine functions each depend on onlyone of the summation indices. The expression E2 can therefore berewritten as: ##EQU5##

This is the equivalent of a first one-dimensional IDCT performed on theproduct of all terms that depend on k and n, followed, after astraightforward standard data transposition, by a second one-dimensionalIDCT using as inputs the outputs of the first IDCT operation.

Definition of the 1-D IDCT

A 1-dimensional, N-point IDCT (where N is an even number) is defined bythe following expression: ##EQU6## and when y(n) are the N inputs to theinverse transformation function and x(k) are its outputs. As in the 2-Dcase, the formula for the DCT has the same structure under the summationsign, but with the normalization constant outside the summation sign andwith the x and y vectors switching places in the equation.

Resolution of a 1-D IDCT

As is shown above, the 2-D IDCT can be calculated using a sequence of1-D IDCT operations separated by a transpose. According to anembodiment, each of these 1-D operations is in turn broken down intosub-procedures that are then exploited to reduce even further therequired size and complexity of the semiconductor implementation.

Normalization of coefficients

As in discussed above, an important design goal for IDCT hardware is thereduction of the required number of multipliers that must be included inthe circuitry. Most methods for calculating the DCT or IDCT thereforeattempt to reduce the number of multiplications needed. According tothis embodiment, however, all the input values are deliberately scaledupward by a factor of √2. In other words, using the method according tothis embodiment, the right-hand side of the IDCT expression (E4) isdeliberately multiplied by √2.

According to this embodiment, two 1-D IDCT operations are performed inseries (with an intermediate transpose) to yield the final 2-D IDCTresult. Each of these 1-D operations includes a multiplication by thesame √2 factor. Since the intermediate transposition involves noscaling, the result of two multiplications by √2 in series is that thefinal 2-D results will be scaled upward by a factor of √2·√2=2. Toobtain the unscaled value the circuitry need then only divide by two,which, since the values are all represented digitally, can beaccomplished easily by a simple right shift of the data. As is madeclearer below, the upward scaling by √2 in each 1-D IDCT stage and finaldown-scaling by 2 is accomplished by adders, multipliers, and shiftersall within the system's hardware, so that the system places norequirements for scaled inputs on the other devices to which the systemmay be connected. Because of this, the system is compatible with otherconventional devices that operate according to the JPEG or MPEGstandards.

Normalization according to this embodiment thus eliminates the need forhardware multipliers within the IDCT semiconductor architecture for atleast two √2-multiplication operations. As is explained below in greaterdetail, the single additional multiplication step (upward scaling by √2)of the input data in each 1-D operation leads to the elimination of yetother multiplication steps that are required when using conventionalmethods.

Separation of the 1-D IDCT into High and Low-Order outputs

Expression E4 can now be evaluated separately for the N/2 low-orderoutputs (k=0, 1, . . . , N/2-1) and the N/2 high-order outputs (k=N/2,N/2+1, . . . N). For N=8, this means that one can first transform theinputs to calculate y(0), y(1), y(2), and y(3), and then transform theinputs to calculate y(4), y(5), y(6), and y(7).

Introduce the variable k'=(N-1-k) for the high-order outputs (k=N/2+1, .. . , N), so that k' varies from (N/2-1) to 0 as k varies from (N/2+1)to N. For N=8, this means that k'={3,2,1,0} for k={4,5,6,7}. It can thenbe shown that expression E4 can be divided into the following twosub-expressions E5 (which is the same as E4 except for the interval ofsummation) and E6:

Low-order outputs: ##EQU7## where k={0,1, . . . , (N/2-1)}; and where##EQU8## High-order outputs: ##EQU9## where k={N, . . . ,(N/2+1)}→k'={0,1, . . . , (N/2-1)}

(Since c(n)=1 for all high-order terms, c(n) is not included in thisexpression).

Note that both E5 and E6 have the same structure under the summationsign except that the term (-1)^(n) changes the sign of the product underthe summation sign for the odd-numbered inputs (n odd) for the upper N/2output values and except that the y(0) term will be multiplied byc(0)=1/√2.

Separation of the 1-D IDCT into Even and Odd Inputs

Observe that the single sum in the 1-D IDCT expression E4 can also beseparated into two sums: one for the even-numbered inputs (for N=8,y(0), y(2), y(4), and y(6)) and one for the odd-numbered inputs (forN=8, y(1), y(3), y(5), and y(7)). Let g(k) represent the partial sum forthe even-numbered inputs and h(k) represent the partial sum for theodd-numbered inputs. Thus: ##EQU10## where k={0, 1, . . . , (N/2-1)};and ##EQU11## where k={0, 1, . . . , (N/2-1)}.

For N=8, observe that the sums in E7 and E8 both are taken over n={0, 1,2, 3}.

Now recall the known cosine identity:

2·cos A·cos B=cos (A+B)+cos (A-B), and set A=π(2k+1)/2N and B=π(2k+1)(2n+1)/2N. One can then multiply both sides of the expression E8 by:

    2·cos A=1/{2·cos [π(2k+1)/2N]}=C.sub.k.

Note that, since C_(k) does not depend on the summation index n, it canbe moved within the summation sign. Assume then by definition thaty(-1)=0, and note that the cosine function for the input y(7) is equalto zero. The expression for h(k) can then be rewritten in the followingform: ##EQU12## where k={0, 1, . . . , (N/2-1)}.

Note that the "inputs" [y(2n+1)+y(2n-1)] imply that, in calculatingh(k), the odd input terms are paired to form N/2 "paired inputs"p(n)=[y(2n+1)+y(2n-1)].

For N=8, the values of p(n) are as follows: ##EQU13##

Expression E9 for h(k) can then be represented by the following:##EQU14## where k={0, 1, . . . , (N/2-1)}.

Observe now that the cosine term under the summation sign is the samefor both g(k) and h(k), and that both have the structure of a 1-D IDCT(compare with expression E5). The result of the IDCT for the odd kterms, that is, for h(k), however, is multiplied by the factor C_(k)=1/{2·cos [π(2k+1)/2N]}. In other words, g(k) is an N/2-point IDCToperating on even inputs y(2n) and h(k) is an N/2-point IDCT operatingon [y(2n+1)+y(2n-1)] where y(-1)=0 by definition.

Now introduce the following identities:

yn=y(n);

c1=cos (π/8);

c2=cos (2π/8)=cos (π/4)=1/√2

c3=cos (3π/8);

d1=1/[2·cos (π/16)];

d3=1/[2·cos (3π/16)];

d5=1/[2·cos (5π/16)]; and

d7=1/[2·cos (7π/16)].

Further introduce scaled cosine coefficients as follows:

c1s=√2·cos (π/8);

c3s=√2·cos (3π/8);

Using the known evenness (cos (-φ)=cos (φ)) and periodicity (cos(π-φ)=-cos (φ)) of the cosine function, expressions E7 and E8 can thenbe expanded for N=8 to yield (recall also that c(0) is 1/√2): ##EQU15##and

    h(0)=d1·{y1+(y1+y3)c1+(y3+y5)c2+(y5+y7)c3}=d1/√2·{√2·y1+(y1+y3)·c1s+(y3+y5)+(y5+y7)·c3s}

    h(1)=d3·{y1+(y1+y3)c3-(y3+y5)c2-(y5+y7)c1}=d3/√2·{√2·y1+(y1+y3)·c3s-(y3+y5)-(y5+y7)·c1s}

    h(2)=d5·{y1-(y1+y3)c3-(y3+y5)c2+(y5+y7)c1}=d5/√2·{√2·y1-(y1+y3)·c3s-(y3+y5)+(y5+y7)·c1s}

    h(3)=d7·{y1-(y1+y3)c1+(y3+y5)c2-(y5+y7)c3}=d7/√2·{√2·y1-(y1+y3)·c1s+(y3+y5)-(y5+y7)·c3s}

Now recall that, according to this embodiment, all values are scaledupward by a factor of √2 for both the DCT and IDCT operations. In otherwords, according to the embodiment, both h(k) and g(k) are multiplied bythis scaling factor. The g(k) and h(k) expressions therefore become:

(E11):

    g(0)=y0+y2·c1s+y4+y6·c3s

    g(1)=y0+y2·c3s-y4-y6·c1s

    g(2)=y0-y2·c3s-y4+y6·c1s

    g(3)=y0-y2·c1s+y4-y6·c3s

and

(E12):

    h(0)=d1{√2·y1+(y1+y3)·c1s+(y3+y5)+(y5+y7).multidot.c3s}

    h(1)=d3{√2·y1+(y1+y3)·c3s-(y3+y5)-(y5+y7) ·c1s}

    h(2)=d5{√2·y1-(y1+y3)·c3s-(y3+y5)+(y5+y7).multidot.c1s}

    h(3)=d7{√2·y1-(y1+y3)·c1s+(y3+y5)-(y5+y7).multidot.c3s}

Notice that, since c2=cos (π/4)=1/√2, multiplication by √2 gives a"scaled" c2 value=1. By scaling the expressions (corresponding to upwardscaling of the values of the video absolute and frequency values)according to this embodiment, it is thus possible to eliminate the needto multiply by c2 altogether. Furthermore, only two cosine terms need tobe evaluated, c1s and c3s, both of which are constant coefficients sothat general utility multipliers are not needed. This in turn eliminatesthe need for the corresponding hardware multiplier in the semiconductorimplementation of the IDCT operations.

The similarity in structure of g(k) and h(k) can be illustrated byexpressing these sets of equations in matrix form. Let C be the 4×4cosine coefficient matrix defined as follows: ##EQU16## where D=diag[d1,d3, d5, d7]=the 4×4 matrix with d1, d3, d5 and d7 along the diagonal andwith all other elements equal to zero. As E14 and E15 show, theprocedures for operating on even-numbered inputs to get g(k) and foroperating on the odd-numbered inputs to get h(k) both have the commonstep of multiplication by the cosine coefficient matrix C. To get h(k),however, the inputs must first be pairwise summed (recalling thaty(-1)=0 by definition), y(1) must be premultiplied by √2, and the resultof the multiplication by C must be multiplied by D.

As the expressions above also indicate, the N-point, 1-D IDCT (see E4)can be split into two N/2-point, 1-D IDCTs, each involving common coreoperations (under the summation sign) on the N/2 odd (grouped) and N/2even input values. The expressions above yield the following simplestructure for the IDCT as implemented in this embodiment:

Low-order outputs (for N=8, outputs k={0, 1, 2, 3}): (E16):

    y(k)=g(k)+h(k)

High-order outputs (for N=8, outputs k={4, 5, 6, 7}):

(E17):

    y(k)=y(N-1-k')=g(k')-h(k')

Note that g(k) operates directly on even input values to yield outputvalues directly, whereas h(k') involves grouping of input values, aswell as multiplication by the values d1, d3, d5 and d7.

As always, the designer of an IDCT circuit is faced with a number oftrade-offs, such as size versus speed and greater number of implementeddevices versus reduced interconnection complexity. For example, it isoften possible to improve the speed of computation by including more, ormore complicated, devices on the silicon chip, but this obviously makesthe implementation bigger or more complex. Also, the area available ordesired on the IDCT chip may limit or preclude the use of sophisticated,complicated, designs such as "look-ahead" adders.

Standards of Accuracy

Assuming infinite precision and accuracy of all calculations, and thusunlimited storage space and calculation time, the image recreated byperforming the IDCT on DCT-transformed image data would reproduce theoriginal image perfectly. Of course, such perfection is not to be hadusing existing technology.

In order to achieve some standardization, however, IDCT systems are atpresent measured according to a standardized method put forth by theComite Consultatif International Telegraphique et Telephonique ("CCITT")in "Annex 1 of CCITT Recommendation H.261--Inverse Transform AccuracySpecification". This test specifies that sets of 10,000 8-by-8 blockscontaining random integers be generated. These blocks are then DCT andIDCT transformed (preceded or followed by predefined rounding, clippingand arithmetic operations) using predefined precision to produce 10,000sets of 8-by-8 "reference" IDCT output data.

When testing an IDCT implementation, the CCITT test blocks are used asinputs. The actual IDCT transformed outputs are then comparedstatistically with the known "reference" IDCT output data. Maximumvalues are specified for the IDCT in terms of peak, mean, mean squareand mean mean error of blocks as a whole and individual elements.Furthermore, the IDCT must produce all zeros out if the correspondinginput block contains all zeros, and the IDCT must meet the samestandards when the sign of all input data is changed. Implementations ofthe IDCT are said to have acceptable accuracy only if their maximumerrors do not exceed the specified maximum values when these tests arerun.

Other known standards are those of the Institute of Electrical andElectronic Engineers ("IEEE"), in "IEEE Draft Standard Specification forthe Implementation of 8 by 8 Discrete Cosine Transform", P1180/D2, Jul.18, 1990; and Annex A of "8 by 8 Inverse Discrete Cosine Transform", ISOCommittee Draft CD 11172-2. These standards are essentially identical tothe CCITT standard described above.

Hardware Implementation

FIG. 1 is a simplified block diagram that illustrates the data flow ofthe IDCT method according to one embodiment (although the hardwarestructure, as is illustrated and explained below, is made more compactand efficient). In FIG. 1, the inputs to the system such as Y[0] andY[4], and the outputs from the system, such as X[3] and X[6], are shownas being conveyed on single lines. It is to be understood that each ofthe single-drawn lines in FIG. 1 represents several conductors in theform of data buses to convey, preferably in parallel, the several-bitwide data words that each input and output corresponds to.

In FIG. 1, large open circles represent two-input, single-output adders,whereby a small circle at the connection point of an input with theadder indicates that the complement of the corresponding input word isused. Adders with such a complementing input thus subtract thecomplemented input from the non-complemented input. For example,although the output T0 from the upper left adder will be equal toY[0]+Y[4] (that is, T0=Y0+Y4, the adder with the output T1 forms thevalue Y0+(-1)·Y4=Y0-Y4. Adders with a single complementing input cantherefore be said to be differencing components.

Also in FIG. 1, constant-coefficient multipliers are represented bysolid triangles in the data path. For example, the input Y1 passesthrough a √2 multiplier before entering the adder to form B0.Consequently, the intermediate value T3=Y2·T3=Y2·cls+Y6·c3s, and theintermediate value B2=p1·c3s-p3·cls=(Y1+Y3)·c3s-(Y5+Y7)·cls. Byperforming the indicated additions, subtractions, and multiplications,one will see that the illustrated structure implements the expressionsE11 and E12 for g(0) to g(3) and h(0) to h(3).

FIG. 1 illustrates an important advantage of the embodiment. As FIG. 1shows, the structure is divided into four main regions: a pre-commonblock PREC that forms the paired inputs p(k) and multiplies the inputY(1) by √2; a first post-common block POSTC1 that includes fourmultipliers for the constants d1, d3, d5, d7 (see expression E12); asecond post-common block POSTC2 that sums the g0 to g3 terms and the h0to h3 terms for the low order outputs, and forms the difference of theg0 to g3 terms and the h0 to h3 terms for the high-order outputs (seeexpressions E16 and E17); and a common block CBLK (described below).

As expressions E14 and E15 indicate, by manipulating the input signalsaccording to the embodiment, processing both the even-numbered andodd-numbered input signals involves a common operation represented bythe matrix C. This can be seen in FIG. 1, in which the common block CBLKis included in both the even and odd data paths. In the processingcircuitry according to the embodiment, the common operations performedon the odd- and even-numbered inputs are carried out by a singlestructure, rather than the duplicated structure illustrated in FIG. 1.

To understand the method of operation and the advantages of certaindigital structures used in the embodiment, it is helpful to understandwhat a "carry word" is, and how it is generated.

In performing the two most common arithmetic operations, addition andmultiplication, digital devices need to deal with the problem of "carrybits". As a simple example, note that the addition of two binary numbersis such that 1+1=0, with a carry of "1", which must be added into thenext higher order bit to produce the correct result "10" (the binaryrepresentation of the decimal number "2"). In other words, 01+01=00 (the"sum" without carry) +10 (the carry word); adding the "sum" to the"carry word", one gets the correct answer 00+10=10.

As a decimal example, assume that one needs to add the numbers "436" and"825". The common procedure for adding two numbers by hand typicallyproceeds as follows:

1) Units: "6" plus "5" is "1", with a carry of "1" into the "tens"position--Sum: 1, Carry-In: 0, Carry-Out: 1;

2) Tens: "3" plus "2" is "5", plus the "1" carried from the precedingstep, gives "6", with no carry--Sum: 5, Carry-In: 1, Carry-Out: 0

3) Hundreds: "4" plus "8" is "2", with a carry of 1 into the thousands,but with no carry to be added in from the previous step;

Sum: 2, Carry-In: 0, Carry-Out: 1

4) Thousands: "0" plus "0" is "0", plus the "1" carried from thehundreds, gives "1".

Sum: 0, Carry-In: 1, Carry-Out: 0

The answer, "1261", is thus formed by adding the carry-in sum for eachposition to the sum for the same position, with the carry-in to eachposition being the carry-out of the adjacent lower-order position. (Notethat this implies that the carry-in to the lowest order position isalways a "0".) The problem, of course, is that one must wait to add the"4" and "8" in the hundreds place until one knows whether there will bea carry-in from the tens place. This illustrates a "ripple adder", whichoperates essentially in this way. A ripple adder thus achieves a "final"answer without needing extra storage elements, but it is slower thansome other designs.

One such alternative design alternative design is known as "carry-save",in which the sum of two numbers for each position is formed by storing apartial sum or result word (in this example, 0251) and the carry valuesin a different word (here, 1010). The full answer is then obtained by"resolving" the sum and carry words in a following addition step. Thus,0251+1010=1261. Note that one can perform the addition for everyposition at the same time, without having to wait to determine whether acarry will have to be added in, and the carry word can be added to thepartial result at any time as long as it is saved.

Since the resolving operations typically require the largest proportionof the time required in each calculation stage, speeding up theseoperations has a significant effect on the overall operating speed whilerequiring only a relatively small increase in the size of the transform.Carry-save multipliers thus are usually faster than those that useripple adders in each row, but this gain in time comes at the cost ofgreater complexity. since the carry word for each addition in themultiplier must be either stored or passed down to the next addition.Furthermore, in order to obtain the final product of a multiplication,the final partial sum and final carry word will have to be resolved,normally by addition in a ripple adder. Note, however, that only oneripple adder will be needed, so that the time savings are normallyproportional to the size of the multiplication that must be performed.Furthermore, note that a carry word may be treated as any other numberto be added in and as long as it is added in at some time before thefinal multiplication answer is needed, the actual addition can bedelayed.

In this embodiment, this possibility of delaying resolution is used tosimplify the design and increase the throughput of the IDCT circuitry.Also, certain bits of preselected carry words are, optionally,deliberately forced to predetermined values before resolution in orderto provide greater expected accuracy of the IDCT result based on astatistical analysis of test runs of the invention on standard test datasets.

FIG. 2 is a block diagram that illustrates a preferred structure. Inthis preferred embodiment of the invention, the even- and odd- numberedinputs are time-multiplexed and are processed separately in the commonblock CBLK. The inputs may be processed in either order.

In FIG. 2, the notation Y[1,0], Y[5,4], Y[3,2] and Y[7,6] is used toindicate that the odd-numbered inputs Y1, Y3, Y5, Y7 preferably passthrough the calculation circuitry first, followed by the even-numberedinputs Y0, Y2, Y4, Y6. This order is not essential to the embodiment;nonetheless, as is explained below, certain downstream arithmeticoperations are performed only on the odd-numbered inputs, and byentering the odd-numbered input values first, these downstreamoperations can be going on at the same time that arithmetic operationscommon to all inputs are performed upstream on the even-numbered inputs.This reduces the time that several arithmetic devices otherwise wouldremain idle.

Similarly, the notation X[0,7], X[1,6], X[3,4], X[2,5] is used toindicate that the low-order outputs X0, X1, X2, X3 are output first,followed by the high-order outputs X4, X5, X6, X7. As FIGS. 1 and 2illustrate, the inputs are preferably initially not grouped in ascendingorder, although this is not necessary according to the invention. Thus,reading from top to bottom, the even-numbered inputs are Y0, Y4, Y2, andY6 and the odd-numbered inputs are Y1, Y5, Y3, and Y7. Arranging theinput signals in this order makes possible the simple "butterfly" datapath structure shown in FIGS. 1 and 2 and greatly increases theinterconnection efficiency of the implementation of the invention insilicon semiconductor devices.

In FIG. 2, adders and subtractors are indicated by circles containingeither a "+" (adder), "-" (subtractor, that is, an adder with onecomplementing input), or "±" (resolving adder/subtractor, which is ableto switch between addition and subtraction). The left-most adders andsubtractors in the common block CBLK are preferably carry-save addersand subtractors, meaning that their output upon addition/subtraction ofthe two m-bit input words is the m-bit partial result in parallel withthe m-bit or (m-1)-bit word containing the carry bits of theaddition/subtraction. In other words, the first additions andsubtractions in the common block CBLK are preferably unresolved, meaningthat the addition of the carry bits is delayed until a subsequentprocessing stage. The advantage of this is that such carry-saveadders/subtractors are faster than conventional resolvingadders/subtractors since they do not need to perform the final additionof the carry-bit word to the result. Resolving adders may, however, alsobe used in order to reduce the bus width at the outputs of the adders.

FIG. 2 also illustrates the use of one- and two-input latches in thepreferred embodiment of the invention. In FIG. 2, latches areillustrated as rectangles and are used in both the pre-common block PRECand the post-common block POSTC. Single-input latches are used at theinputs of the multipliers D1, D3, D5 and D7, as well as to latch theinputs to the resolving adders/subtractors that generate the outputsignals X0 to X7. As FIG. 2 illustrates, the inputs to these resolvingadders/subtractors are the computed g(k) and h(k) values correspondingto the respective outputs from latches g[0,7], g[1,6], g[3,4] andg[2,5], and h[0,7], h[1,6], h[3,4] and h[2,5]. As such, the resolvingadders/subtractors perform the addition or subtraction indicated inexpressions E16 and E17 above.

As is explained above, the even-numbered inputs Y0, Y2, Y4, and Y6 donot need to be paired before being processed in the common block CBLK.Not only do the odd-numbered inputs require such pairing, however, butthe input Y1 must also be multiplied by √2 in order to ensure that theproper input values are presented to the common block CBLK. Thepre-common block PREC, therefore, includes a 2-input multiplexing("mux") latch C10, C54, C32 and C76 for each input value. One input tothe 2-input mux latch is consequently tied directly to the unprocessedinput values, whereas the other input is received from the resolvingadders and, for the input Y1, the resolving √2-multiplier. The correctpaired or unpaired inputs can therefore be presented to the common blockCBLK easily by simple switching of the multiplexing latches betweentheir two inputs.

As FIG. 2 illustrates, the √2-multiplier and the multipliers D1, D3, D5,D7 preferably resolve their outputs, that is, they generate results inwhich the carry bits have been added in to generate a complete sum. Thisensures that the outputs from the multipliers have the same bus width asthe un-multiplied inputs in the corresponding parallel data paths.

The preferred embodiment of the common block also includes one "dummy"adder and one "dummy" subtractor in the forward data paths for Y[1,0]and Y[5,4], respectively. These devices act to combine the two inputs(in the case of the dummy subtractor, after 2's-complementing the oneinput) in such a way that they are passed as parallel outputs. In thesecases, the one input is manipulated as if it contained carry bits, whichare added on in the subsequent processing stage. The correspondingaddition and subtraction is thus performed, although it is delayed.

This technique reduces the resources needed in the upper two data pathssince a full scale adder/subtractor need not be implemented for thesedevices. The "combiners" thus act as adder and subtractors and can beimplemented either as simple conductors to the next device (foraddition), or as a row of inverters (for subtraction), which requireslittle or no additional circuitry.

The use of such combiners also means that the outputs from the initialadders and subtractors in the common block CBLK will all have the samewidth and will be compatible with the outputs of the carry-saveadder/subtractors found in the bottom two data paths, with which theyform inputs to the subsequent resolving adders and subtractors in thecommon block CBLK.

As is mentioned above, the even-numbered inputs are processed separatelyfrom the odd-numbered in this preferred embodiment of the invention.Assume that the odd-numbered inputs are to be processed first.Supervisory control circuitry (not shown in FIG. 2) then applies theodd-numbered input words to the pre-common block PREC, and selects thelower inputs (viewed as in FIG. 2) of the multiplexing latches C10, C54,C32, C76, which then will store the paired values p0 to p3 (see FIG. 1and the definition of p(n) above). The latches Lh0, Lh1, Lh3, and Lh2are then activated to latch the values H0, H1, H3, and H2, respectively.

The supervisory control circuitry then latches and then selects theupper inputs of the two-input multiplexing latches C10, C54, C32 and C76in the pre-common block PREC and applies the even-numbered input wordsto these latches. Since the even-numbered inputs are used to form thevalues of g0 to g3, the supervisory control circuitry then also opensthe latches Lg0 to Lg3 in the post-common block POSTC, which store theg(k) values.

Once the g(k) and h(k) values are latched, the post-common block POSTCoutputs the high-order output signals X7, X6, X5 and X4 by switching theresolving adder/subtractors to the subtraction mode. The low-orderoutput signals X3, X2, X1, and X0 are then generated by switching theresolving adders/subtractors to the addition mode. Note that the outputdata can be presented in an arbitrary order, including natural order.

The preferred multiplexed implementation illustrated in greatlysimplified, schematic form in FIG. 2, performs the same calculations asthe non-multiplexed structure illustrated in FIG. 1. The number ofadders, subtractors and multipliers in the common block CBLK is,however, cut in half and the use of dummy adder/subtractors furtherreduces the complexity of the costly arithmetic circuitry.

FIG. 3 illustrates the main components and data lines of an actualimplementation of the IDCT circuit according to the embodiment. The maincomponents include the pre-common block circuit PREC, the common blockcircuit CBLK, and the post-common block POSTC. The system also includesa controller CNTL that either directly or indirectly applies input,timing and control signals to the pre-common block PREC and post-commonblock POSTC.

In the preferred embodiment of the invention, the input and outputsignals (Y0 to Y7 and X0 to X7, respectively) are 22 bits wide. Testshave indicated that this is the minimum width that is possible thatstill yields acceptable accuracy as measured by existing industrystandards. As is explained in greater detail below, this minimum widthis achieved in part by deliberately forcing certain carry words inselected arithmetic devices to be either a "1" or a "0". This bitmanipulation, corresponding to an adjustment of certain data words, iscarried out as the result of a statistical analysis of the results ofthe IDCT system according to the embodiment after using the embodimentfor IDCT transformation of known input test data. By forcing certainbits to predetermined values, it was discovered that the effects ofrounding and truncation errors could be reduced, so that the spatialoutput data from the IDCT system could be made to deviate less from theknown, "correct" spatial data. The invention is equally applicable,however, to other data word lengths since the components used in thecircuit according to the embodiment all can be adapted to different buswidths using known methods.

Although all four inputs that are processed together could be inputsimultaneously to the pre-common block PREC along 88 parallel conductors(4×22), pixel words are typically converted one at a time from theserial transmission data. According to the embodiment, input data wordsare therefore preferably all conveyed serially over a single, 22-bitinput bus and each input word is sequentially latched at the properinput point in the data path. In FIG. 3, the 22-bit input data bus islabelled T₋₋ IN[21:0].

In the Figures and in the discussion below, the widths of multiple-bitsignals are indicated in brackets with the high-order bit to the left ofa colon ":" and the least significant bit (LSB) to the right of thecolon. For example, the input signal T₋₋ IN[21:0] is 22 bits wide, withthe bits being number from 0 to 21. A single bit is identified as asingle number within square brackets. Thus, T₋₋ IN[1] indicates the nextto least significant bit of the signal T₋₋ IN.

The following control signals are used to control the operation of thepre-common block PREC in the preferred embodiment of the invention:

IN₋₋ CLK, OUT₋₋ CLK: The system according to the embodiment preferablyuses a non-overlapping two-phase clock. The signals IN₋₋ CLK and OUT₋₋CLK are accordingly the signals for the input and output clock signals,respectively. These clock signals are used to enable alternating columnsof latches that hold the values of input, intermediate, and outputsignals.

LATCH10, LATCH54, LATCH32, LATCH76: Preferably, one 22-bit word is inputto the system at a time. On the other hand, four input signals areprocessed at a time. Each input signal must therefore be latched at itsappropriate place in the architecture before processing with three otherinput words. These latch signals are used to enable the respective inputlatches. The signal LATCH54, for example, is first used to latch inputsignal Y5 and later to latch input signal Y4, which enters thepre-common block PREC at the same point as the input signal Y5 (see FIG.2) but during a subsequent processing stage.

LATCH: Once the four even- or odd-numbered input signals are latchedinto the pre-common block PREC, they are preferably shifted at the sametime to a subsequent column of latches. The signal LATCH is used toenable a second column of input latches that hold the four input valuesto be operated on by the arithmetic devices in the pre-common blockPREC.

SEL₋₋ BYP, SEL₋₋ P: As FIG. 2 illustrates, the even-numbered inputsignals that are latched into the latches C10, C54, C32, and C76 shouldbe those that bypass the adders and the √2 resolving multiplier. Theodd-numbered input signals, however, must first be paired to form thepaired inputs p(n), and the signal Y1 must be multiplied by √2. Thecontrol signal SEL--BYP is used to select the ungrouped, bypass inputsignals (the even-numbered inputs), whereas the signal SEL₋₋ P isactivated in order to select the paired input signals. These signals arethus used to control gates that act as multiplexers to let the correctsignals pass to the output latches of the pre-common block PREC.

As is explained above, not arranging the inputs in strictly ascendingorder leads to a simplified "butterfly" bus structure with highinterconnection efficiency. As is explained above, the odd inputs arepreferably applied as a group to the pre-common block first, followed bythe even-numbered inputs, but any order may be used, however, suitablelatch arrangements being provided to process the odd-numbered andeven-numbered inputs are separately, or at least in separate regions ofthe circuit.

The supervisory control circuitry also generates timing and controlsignals for the post-common block POSTC. These control signals are asfollows:

EN₋₋ BH, EN₋₋ GH: Considering for the moment FIG. 1, the outputs fromthe common block CBLK, after processing of the odd-numbered inputs, areshown as H0, H1, H3 and H2. These signals are then sent to thecoefficient multipliers, d1, d3, d7, d5, respectively, in the firstpost-common block POSTC 1. The signal EN₋₋ BH is used to enable latchesthat hold signals corresponding to H0 to H3. The signal EN₋₋ GH is usedto enable latches that hold the g0 to g3 values, as well as latches thathold the h0 to h3 values after they have been multiplied in thecoefficient multipliers.

ADD, SUB: As FIG. 2 illustrates, the embodiment includes a bank ofresolving adders/subtractors that sum and difference g(k) and h(k)values in order to form the low-order and high-order outputs,respectively. The signals ADD, SUB are used to set the resolvingadders/subtractors in the addition and subtraction modes, respectively.

EN₋₋ O: This signal is used to enable output latches that latch theresults from the resolving adders/subtractors.

MUX₋₋ OUT70, MUX₋₋ OUT61, MUX₋₋ OUT43, MUX₋₋ OUT52: The output data fromthe system is preferably transmitted over a single 22-bit output bus, sothat only one output value (X0 to X7) is transferred at a time. Thesesignals are activated sequentially to select which of the four latchedoutput values is to be latched into a final output latch. These signalsthus act as the control signals for a 4-to-1 multiplexer.

T₋₋ OUT[21:0]: This label indicates the 22-bit output signal from thepost-common block POSTC.

The output signals from the pre-common block PREC are latched to formthe inputs signals to the common block CBLK. In FIG. 3, the outputsignals from the pre-common block PREC are represented as the four22-bit data words CI10[21:0], CI54[21:0], CI32[21:0], CI76[21:0], whichbecome the input signals IN[0], IN[1], IN[3], IN[2], respectively, tothe common block CBLK.

As FIG. 3 shows, the four 22-bit results from the common block CBLK aretransferred in parallel as output signals OUT0[21:0], OUT1[21:0],OUT3[21:0], OUT2[21:0], which are then latched as the input signals ofthe post-common block POSTC as CO70[21:0], CO61[21:0], CO43[21:0],CO52[21:0].

One should note in particular that no control signals are required forthe common block CBLK. Because of the unique structure of the IDCTsystem in this example, the common block of operations can be performedas pure logic operations, with no need for clock, timing or controlsignals. This further reduces the complexity of the device. One shouldnote that certain applications (particularly those in which there isplenty of time to perform all needed arithmetic operations) thepre-common and post-common blocks PREC, POSTC may also be arranged tooperate without clock, timing or control signal.

FIG. 4 is a block diagram of the pre-common block PREC. In this andfollowing figures, the notation "S1[a], S2[b], . . . , SM[Z]," where Sis an arbitrary signal label and a, b, . . . , z are integers within therange of the signal's bus width, indicates that the selected bits a, b,. . . , z from the signals S1, S2, . . . , SM are transferred inparallel over the same bus, with the most significant bits (MSBs) beingthe selected bits "a" of the signal S1, and the least significant bits(LSBs) being the selected bits "z" of signal SM. The selected bits donot have to be individual bits, but rather, entire or partial multi-bitwords may also be transmitted along with other single bits or completeor partial multi-bit words. In the figures, the symbol S will bereplaced by the corresponding signal label.

For example, in FIG. 4, a √2-multiplier is shown as R2MUL. The "save" or"unresolved sum" output from this non-resolving multiplier is indicatedas the 21-bit word M5S[20:0]. The "carry" output from the multiplierR2MUL is shown as the 22-bit word M5C[21:0], which is transferred overthe bus to the "b" input of a carry-save resolving adder M5A. (Recallthat a "0" is inserted as an MSB to the least significant 21 bits of thesave output, however, before being applied to the "a" input of theresolving adder M5A. This is indicated in FIG. 4 by the notationGND,M5S[20:0]). In other words, the conductor corresponding to the MSBinput to the adder M5A is forced to be a "0" by tying it to ground GND.

In order to understand why a "0" is thus inserted as the 22'nd bit ofthe "sum" output, observe that if the partial sum of a multiplication isn places wide, the carry word will normally also have n places. Inadding the carry word to the partial sum, however, the carry word isshifted one place to the left relative to the partial sum. The carryword therefore extends to n+1 places, with a valid data bit in then+1'th position and a "0" in the least significant position (since thereis nothing before this position to produce a carry bit into the unitsposition). If these two words are used as inputs to a resolving binaryadder, care must be taken to ensure that the bits (digits) of the carryword are properly aligned with the corresponding bits of the partialsum. This also ensures that the decimal point (even if only implied, asin integer arithmetic) is kept "aligned" in both words. Assuming theinputs to the adder are n+1 bits wide, a "0" can then be inserted intothe highest-order bit of all n-bit positive partial sum words to providean n+1-bit input that is aligned with the carry word at the other input.

As is described above, the four inputs that are processed at a time inthe pre-common block PREC are transferred over the input bus T₋₋IN[21:0]. This input bus is connected to the inputs of four inputlatches IN10L, IN54L, IN32L, and IN76L. Each respective latch is enabledonly when the input clock signal IN₋₋ CLK and the corresponding latchselection signal LATCH10, LATCH54, LATCH32, LATCH76 are high. The fourinputs can therefore be latched into their respective input latches infour periods of the IN₋₋ CLK signal by sequential activation of thelatch enabling signals LATCH10, LATCH54, LATCH32, LATCH76. During thistime, the LATCH signal should be low (or on a different phase) to enablethe input latches IN10L, IN54L, IN32L, IN76L to stabilize and latch thefour input values.

An example of the timing of the latches is illustrated in FIG. 7a. Oncethe four input signals are latched in the preferred order, they arepassed to a second band of latches L10L, L54L, L32L, L76L. These secondlatches are enabled when the signals OUT₋₋ CLK and LATCH are high. Thissignal timing is also illustrated in FIG. 7a.

Note that the system does not have to delay receipt of all eight inputwords. Once all the even or odd input words are received and latched inIN10L, IN54L, IN32L and IN76L, they can be transferred at the next highperiod of OUT₋₋ CLK to the latches L10L, L54L, L32L and L76L. This thenfrees the IN latches, which can begin to receive the other four inputsignals without delay at the next rising edge of IN₋₋ CLK.

The 2-digit suffix notation [10, 54, 32, 76] used for the variouscomponents illustrated in the figures indicates that odd-numberedsignals are processed first, followed by the even-numbered signals on asubsequent pass through the structure. As is mentioned above, this orderis not necessary.

Once the four input signals are latched in proper order in the secondlatches L10L, L54L, L32L, L76L, the corresponding values are eitherpassed as inputs to output latches C10L, C54L, C32L, and C76L onactivation of the selected by pass signal SEL₋₋ BYP, or they are passedas paired and multiplied inputs to the same output latches uponactivation of the "select p" signal SEL₋₋ P. In other words, all signalsare passed, both directly and indirectly, via arithmetic devices, to theoutput latches C10L, C54L, C32L, C76L of the pre-common block PREC. Theproper values, however, are loaded into these latches by activation ofthe "select bypass" signal SEL₋₋ BYP (for the even-numbered inputs Y0,Y2, Y4, Y6) or the "select p" signal SEL₋₋ P (for the odd-numberedinputs Y1, Y3, Y5, and Y7). The desired timing and order of these andother control signals is easily accomplished in a known manner by properconfiguration and/or [micro-] programming of the controller CNTL.

The uppermost input value at the output of latch L10L is passed first tothe √2-multiplier R2MUL and then to the resolving adder M5A as indicatedabove. The output from the resolving adder M5A is shown as M5[21:0],which corresponds to the 22-bit value p0 shown in FIG. 1. The 22-bitsignal M5[21:0] is thus the equivalent of the resolved multiplication ofthe output from the latch L10L by √2. The outputs from the other threelatches L54L, L32L, L76L are also transferred to corresponding outputlatches C54L, C32L, and C76L, respectively, both directly via 22-bitlatch buses LCH54[21:0], LCH32[21:0], LCH76[21:0] and indirectly to theoutput latches via resolving adders P2A P1A, and P3A, respectively.

Each resolving adder P2A, P1A, P3A has two inputs, "a" and "b". Foradder P2A, the one input is received from the latch L32L, and the otherinput is received from the latch L54L. For input values Y5 (latched inL54L) and Y3 (latched in L32L), the output from the adder P2A willtherefore be equal to Y5+Y3, which, as is shown above, is equal to p(2).The adders thus "pair" the odd-numbered inputs to form the paired inputvalues p(1), p(2), and p(3). Of course, the even-numbered input signalslatched in L54L, L32L, L76L will also pass through the resolving addersP2A, P1A, and P3A, respectively, but the resulting p "values" will notbe passed to the output latches C54L, C32L, and C76L because the "selectp" signal SEL₋₋ P will not be activated for even-numbered inputs.

The values that are latched in the output latches C10L, C54L, C32L, andC76L upon activation of the input clock signal IN₋₋ CLK will thereforebe equal to either the even-numbered inputs Y0, Y2, Y4, Y6 or the pairedinput values P0, P1, P2, P3 for the odd-numbered inputs. One shouldrecall that the input Y(1) is paired "paired" with the value Y(-1),which is assumed to be zero. In FIG. 4, this assumption is implementedby not adding anything to the value Y1; rather, Y1 is only multiplied by√2, as is shown in FIGS. 1 and 2.

FIG. 5 illustrates the preferred architecture of the common block CBLKaccording to the embodiment. Because of the various multiplications andadditions in the different system blocks, it is necessary oradvantageous to scale down the input values to the common block beforeperforming the various calculations; this ensures a uniform position forthe decimal point (which is implied for integer arithmetic) forcorresponding inputs to the various arithmetic devices in the system.

The input values IN0[21:0] and IN1[21:0] are accordingly scaled down bya factor of four, which corresponds in digital arithmetic to a rightshift of two bits. In order to preserve the sign of the number (keeppositive values positive and negative values negative) in binaryrepresentation, the most significant bits of the resulting right-shiftedword; this process is known as "sign extension". Accordingly, the inputvalue IN0 is downshifted by two bits with sign extension to form theshifted input value indicated as IN0[21],IN0[21], IN0[21:2]. The inputvalue IN1[21:1] is similarly sign-extended two places. The input valueIN3 and IN2 (corresponding, respectively, to inputs Y[3,2] and Y[7,6])are shifted right one position with sign extension. The third input istherefore shifted and extended as IN3[21], IN3[21:1]. The input IN2 issimilarly shifted and extended to form IN2[21], IN2[21:1]. Theseone-position shifts correspond to truncated division by a factor of two.

As FIG. 2 shows, the inputs IN3, IN2 are those which must be multipliedby the scaled coefficients c1s and c3s. Each input IN3 and IN2 must bemultiplied by each of the scaled coefficients. As FIG. 5 illustrates,this is implemented by the four constant-coefficient carry-savemultipliers MULC1A, MULNC1S, MULC3S3, and MULC3S2. One should note thatthe bottom multiplier for IN2 is an inverting multiplier MULNCIS, thatis, its output corresponds to the negative of the value of the inputmultiplied by the constant C1S. The value latched in C76 is thussubtracted from the value latched in C32 (after multiplication by C3S).By providing the inverting multiplier MULNC1S, this subtraction isimplemented by adding the negative of the corresponding value, which isequivalent to forming a difference. This allows the use of identicalcircuitry for the subsequent adders, but a non-inverting multiplier maybe used with a following subtractor.

In the illustrated embodiment, four cosine coefficient multipliersMULC1S, MULNC1S, MULC2S3, and MULC3S2 are included. If arrangements aremade for signals to pass separately through multipliers, however, thenecessary multiplications could be implemented using only twomultipliers, one for the c1s coefficient and one for the c3scoefficient.

The multipliers MULC1S, MULNC1S, MULC3S3, and MULC3S2 are preferably ofthe carry-save type, which means that they produce two output words, onecorresponding to the result of the various rows of additions performedwithin a hardware multiplier, and another corresponding to the carrybits generated. The outputs from the multipliers are then connected asinputs to either of two 4-input resolving adders BT2, BT3.

For ease of illustration only, five of the output buses from themultipliers are not drawn connected to the corresponding input buses ofthe adders. These connections are to be understood, and are illustratedby each respective output and input having the same label. Thus, thesave output M1S[20:0] of the multiplier MULC1S is connected to the lower21 bits of the "save-a" input "sa" of the adder BT3.

In FIG. 5, five of the inputs to the adders BT2 and BT3 are shown asbeing "split". For example, the "ca" input of the adder BT2 is shown ashaving IN3[21] over M3C[20:0]. This is to be interpreted to mean that,of the 22-bit input word, IN3[21] is input as the MSB, with the 21 bitsof M3C[20:0] being input as the least significant 21 bits. Similarly,the "sa" (the "save-a" input) of the same adder is shown as being GND,GND over M3S[19:0]. This means that two zeros are appended as the twomost significant bits of this input word. Such appended bits ensure thatthe proper 22-bit wide input words are formed with the proper sign.

The carry-save adders BT2 and BT3 add the carry and save words of twodifferent 22-bit inputs to form a 22-bit output save word T3S[21:0] anda 21-bit output carry word T3C[21:1]. The input to each adder is thus 88bits wide and the output from each adder is 43 bits wide. As FIG. 2indicates, the output from the latch C10 is combined with the outputfrom the latch C54 in the upper-most data path before addition with theoutput from the carry-save adder BT3. The "combination" is not, however,necessary until reaching the following adder in the upper data path.Consequently, as FIG. 5 shows, the shifted and sign-extended input valueIN0 is connected to the upper carry input.

The upper carry input of adder CS0 is connected to the shifted andsign-extended input value IN0, and the shifted and sign-extended inputIN1 is connected as the upper save input of the same adder. In otherwords, IN0 and IN1 are added later in the adder CS0.

The designation "dummy" adder/subtractor used in FIG. 2 thereforeindicates which operation must be performed, although it does notnecessarily have to be performed at the point indicated in FIG. 2.Similarly, the lower dummy subtractor shown in FIG. 2 requires that theoutput from latch C54 be subtracted from the output from latch C10. Thisis the same as adding the output from C10 to the complement of theoutput of C54.

Referring once again to FIG. 5, the complement of the input IN1(corresponding to the output of latch C54 in FIG. 2) is performed by a22-bit input inverter IN1I[21:0] (which generates the logical inverse ofeach bit of its input, bit-for-bit). The complement of IN1value--NIN1[21:0]-- is passed to the upper "save" input of the adderCS1, with the corresponding upper "carry" input being the shifted andsign-extended IN0. The upper portion of the adder CS1 therefore performsthe subtraction corresponding to IN0 minus IN1.

In the lower two data paths shown in FIG. 2, resolving subtractors areused instead of the resolving adders shown in the upper two data pathsat the output of the common block CBLK. Each resolving adder orsubtractor is equivalent to a carry-save adder or subtractor followed bya resolving adder. This is shown in FIG. 5. Subtractors CS2 and CS3 haveas their inputs the processed values of IN0 to IN3 according to theconnection structure shown in FIG. 2.

The 22-bit carry and save outputs from each of the adders/subtractorsCS0-CS3 are resolved in the resolving adders RES0-RES3. Resolution ofcarry and save outputs is well understood in the art of digital designand is therefore not described in greater detail here. As FIG. 5illustrates, the save outputs from the carry-save adders/subtractorsCS0-CS3 are passed directly as 22-bit inputs to the "a"-input of thecorresponding resolving adders RES0-RES3.

As is well known, the 2's-complement of a binary number is formed byinverting each of its bits (changing all "1's" to "0's" and vice versa)and then adding "1". Note that the "1" can be added immediately afterthe bit inversion, or later. The LSB of a carry word will always be a"0", which is implemented in the illustrated embodiment by tying the LSBof the carry words O0C and O1C to ground GND as they are input to theresolving adders RES0 and RES1, respectively. The addition of "1" to thecarry outputs of the subtractors CS2 and CS3 to form 2's-complementedvalues, however, is implemented by tying the LSB of these data words O2Cand O3C to the supply voltage VDD, thus "replacing" the "0" LSB of thecarry word by a "1", which is equivalent to addition by "1".

For the reasons given above, a "0" is appended as the LSB to the 21-bitcarry words from the carry-save adders CS0 and CS1 (by tying the LSB toground GND) and the LSB of the carry words from the carry-savesubtractors CS2 and CS3 is set equal to "one" by tying the correspondingdata line to the supply voltage VDD. The resolving adders RES0-RES3therefore resolve the outputs from the adders/subtractors CS0-CS3 toform the 22-bit output signals OUT0[21:0]-OUT3[21:0].

Two advantages of the IDCT circuitry according to the embodiment can beseen in FIG. 5. First, no control or timing signals are required for thecommon block CBLK; rather, the input signals to the common block arealready processed in such a way that they can be applied immediately tothe pure-logic arithmetic devices in the common block. Second, by properscaling of the data words, integer arithmetic can be used throughout(or, at least, decimal point for all values will be fixed). This avoidsthe complexity and slowness of floating-point devices, with nounacceptable sacrifice of precision.

Yet another advantage of the embodiment is that, by ordering the inputsas shown, and by using the balanced decimated method according to theembodiment, similar design structures can be used at several points inthe silicon implementation. For example, in FIG. 5, the constantcoefficient multipliers MULC1S, MULC3S3, MULC3S2, and MULNC1S all havesimilar structures and receive data at the same point in the data path,so that all four multipliers can be working at the same time. Thiseliminates "bottlenecks" and the semiconductor implementation is thenable to take full advantage of the duplicative, parallel structure. Thecarry-save adders BT2 and BT3 similarly will be able to worksimultaneously, as will the following carry-save adders and subtractors.This symmetry of design and efficient simultaneous utilization ofseveral devices is common throughout the structure according to theembodiment.

FIG. 6 shows the preferred arrangement of the post-common block POSTC.As FIG. 2 shows, the primary functions of the post-common POSTC are toform the h0 to h3 values by multiplying the outputs of the common blockby the coefficients d1, d3, d5, and d7; to add the g(k) and h(k) valuesto form the low-order outputs; and to subtract the h(k) values from thecorresponding g(k) values to form the high-order outputs. Referring nowto both FIG. 2 and FIG. 6, the post-common block POSTC latches thecorresponding outputs from the common block CBLK into latches BH0L,BH1L, BH3L, and BH2L when the BH latches are enabled, the controlcircuitry sets the EN₋₋ BH signal high, and the output clock signalOUTC₋₋ CLK signal goes high. The g(k), g0 to g3 values are latched intocorresponding latches G0L, G1L, G3L and G2L when the control circuitryenables these latches via the signal EN₋₋ GH and the input clock signalIN₋₋ CLK goes high.

The processed odd-numbered inputs, that is, the values h0 to h3, arelatched into latches H0L, H1L, H3L and H2L when the EN₋₋ GH and IN₋₋ CLKsignals are high, via the constant coefficient multipliers D1MUL, D3MUL,D5MUL and D7MUL. These multipliers multiply, respectively, by d1, d3, d5and d7. In the preferred embodiment, these constant-coefficientmultipliers are preferably carry-save multipliers in order to simplifythe design and to increase calculation speed. As FIG. 6 illustrates, the"carry" ("c") outputs from the constant coefficient multipliers areconnected, with certain changes described below, to the a inputs ofresolving adders H0A, H1A, H3A and H2A. The "save" ("s") outputs fromthe coefficient multipliers are similarly, with certain forced changesdescribed below, connected to other input of the corresponding resolvingadder.

As FIG. 6 illustrates, the LSB of the H0 signal is preferably forced tobe a "1" by tying the corresponding line to the supply voltage VDD. TheMSB of the corresponding "save" output for H0 is set to 0 (tied toground GND), and the second bit (corresponding to H0S[1]) is set to "1".The data words from the carry and save outputs of theconstant-coefficient multiplier D3MUL are similarly manipulated andinput to the resolving adder H1A. The advantage of these manipulationsis described below.

All 22-bits of the carry output from the coefficient multipliers D7MULand D5MUL are connected directly to the "a" input of correspondingresolving adders H3A and H2A. The MSB of each multiplier's "save"output, however, is forced to be a "0" by tying the corresponding dataline to ground GND.

The IDCT system described was tested against the CCITT specificationdescribed above. Because of the scaling and other well-known propertiesof digital adders and multipliers, some precision is typically lostduring the various processing stages of the device. The inventorsdiscovered through a statistical analysis of the 10,000-sample test runthat forcing the various bits described above to either "0" or "1"reduced the expected error of the digital transformation. As a result ofthe bit manipulation of the data words, the embodiment achievedacceptable accuracy under the CCITT standard using only 22-bit wide datawords, whereas 24 bits would normally be required to produce equivalentaccuracy.

Because of limited precision, and truncation and rounding errors, thereis typically some inaccuracy in every data word in an IDCT system. Ofcourse, forcing selected bits of a data word to be other than they wouldbe as a natural result of corresponding calculations is deliberatelyintroducing "error". The inventors discovered, however, that the errorthereby systematically introduced into a particular data word at aparticular point in the hardware yielded statistically better overallresults. Bit-forcing may also be applied "within" a multiplication, forexample, by selectively forcing one or more carry bits to predeterminedvalues.

The bit-forcing scheme need not be static, with certain bits alwaysforced to take specified values, but rather a dynamic scheme may also beused. For example, selected bits of a data word may be forced to "1" or"0" depending on whether the word (or even some other data) is even orodd, positive or negative, above or below a predetermined threshold,etc.

Normally, only small systematic changes will be needed to improveoverall statistical performance. Consequently, according to thisembodiment, the LSB's of selected data words (preferably one bit and onedata word at a time, although this is not necessary) are forced to be a"1" or a "0". The CCITT test is run, and the CCITT statistics for therun are compiled. The bit is then forced to the other of "1" or "0", andthe test is rerun. Then the LSB (or LSBs) of other data words are forcedto "1" and "0", and similar statistics are compiled. By examining thestatistics for various combinations of forced bits in various forcedwords, a best statistical performance can be determined.

If this statistically based improvement is not required, however, theoutputs from the constant-coefficient multipliers D1MUL, D3MUL, D5MUL,and D7MUL may be resolved in the conventional manner in the resolvingadders H0A-H3A. The lower 21-bits of the outputs from the resolvingadders H0A-H3A are applied as the upper 21-bits at the input of thecorresponding latches H0L-H3L, with the LSB of these inputs tied toground.

The outputs from the H-latches (H0L-H3L) and the G-latches (G0L-G3L)pairwise form the respective a- and b-inputs to resolvingadder-subtractors S70A, S61A, S43A and S52A. As was indicated above,these devices add their inputs when the ADD signal is high, and subtractthe "b" input from the "a" input when the subtraction enable signal SUBis high. The second bits of the upper two latch pairs H0L, G0L and H1L,G1L are manipulated by multiplexing arrangements in a manner describedbelow.

The outputs from the resolving adder-subtractors S70A, S61A, S43A andS52A are latched into result latches R79L, R61L, R43L and R52L.

In FIG. 6b, the input words to the adder/subtractors S70A and S61A havethe second bits of each input word manipulated. For example, the secondbit of the input word to the "a"-input of the adder/subtractor S70A isG0[21:2], G0[1M], G0[0]. In other words, the second bit of this signalis set to the value G01M. The second bits of the other inputs to theadder/subtractors S70A and S61A are similarly manipulated. This bitmanipulation is accomplished by four 2:1-bit multiplexers H01MUX,G01MUX, H11MUX and G11MUX (shown to the right in FIG. 6b). Thesemultiplexers are controlled by the ADD and SUB signals such that thesecond bit (H01M, G01M, H11M, and G11M) is set to one if the respectiveadder/subtractor S70A, S61A is set to add (ADD is high), and the secondbit is set to its actual latch output value if the SUB signal is set tohigh. Setting of individual bits in this manner is an easilyimplemented, high-speed operation. The preferred embodiment includesthis bit-forcing arrangement since, as is described above, statisticalanalysis of a large number of tests pixel words has indicated that moreaccurate results are thereby obtained. It is not necessary, however, tomanipulate the second bits in this manner, although it gives theadvantage of smaller word width.

The four high- or low-order results are latched in the output latchesR70L R61L, R43L and R52L. The results are sequentially latched into thefinal output latch OUTF under the control of the multiplexing signalsMUX₋₋ OUT70, MUX₋₋ OUT61, MUX₋₋ OUT43, MUX₋₋ OUT52. The order in whichresulting signals are output can therefore be controlled simply bychanging the sequence with which they are latched into the latch OUTF.The output from the latch OUTF is the final 22-bit resulting outputsignal T₋₋ OUT[21:0].

The relationship between the clock and control signals in thepost-common block POSTC is shown in FIGS. 7b and 7c.

As was discussed above, two 1-dimensional IDCT operations may beperformed in series, with an intervening transposition of data, in orderto perform a 2-D IDCT. The output signals from the post-common blockPOSTC are therefore, according to this embodiment, first stored in aknown manner column-wise (or row-wise) in a conventional storage unit,such as a RAM memory circuit (not shown), and are then read from thestorage unit row-wise (column-wise) to be passed as inputs to asubsequent pre-common block and are processed as described above in thisblock, and in common block CBLK and a post-common block POSTC.

Storing by row (column) and reading out by column (row) performs therequired operation of transposing the data before the second 1-D IDCT.The output from the second POSTC will be the desired, 2-D IDCT resultsand can be scaled in a conventional manner by shifting to offset thescaling shifts carried out in the various processing blocks. Inparticular, a right shift by one position will perform the division by 2necessary to offset the two √2 multiplications performed in the 1-D IDCToperations.

Depending on the application, this second IDCT structure (which ispreferably identical to that shown FIG. 3) is preferably a separatesemiconductor implementation. This avoids the decrease in speed thatwould arise if the same circuits were used for both transforms, althoughseparate 1-D transform implementations are not necessary if thepixel-clock rate is slow enough that a single implementation of thecircuit will be able to handle two passes in real time.

In range tests carried out on a prototype of the IDCT arrangementdescribed above, it was found that all intermediate and final valueswere kept well within a known range at each point while still meetingthe CCITT standards. Because of this, it was possible to "adjust"selected values as described above by small amounts (for example, byforcing certain bits of selected data words to desired values) withoutany fear of overflow or underflow in the arithmetic calculations.

The method and system according to the invention can be varied innumerous ways. For example, the structures used to resolve additions ormultiplications may be altered using any known technology. Thus, it ispossible to use resolving adders or subtractors where the preferredembodiment uses carry-save devices with separate resolving adders. Also,the preferred embodiment of the invention uses down-scaling at variouspoints to ensure that all values remain within their acceptable ranges.Down-scaling is not necessary, however, because other precautions may betaken to avoid overflow or underflow.

In a prototype of the invention, certain bits of various data words weremanipulated on the basis of a statistical analysis of test results ofthe system. Although these manipulations reduced the required word widthwithin the system, the various intermediate values may of course bepassed without bit manipulation. Furthermore, although only data wordswere bit-manipulated in the illustrated example of the invention, it isalso possible to manipulate the bits of constant coefficients as welland evaluate the results under the CCITT standard. If a comparison ofthe results showed that it would be advantageous to force a particularbit to a given value, in some cases, one might then be able to increasethe number of "zeros" in the binary representation of these coefficientsin order to decrease further the silicon area required to implement thecorresponding multiplier. Once again, bit manipulation is not necessary.

We claim:
 1. A method for transforming digital signals from a frequencyto a time representation, including grouping the digital signals intogroups of N data input words;CHARACTERIZED by the following steps:a) ina pre-common processing means (PREC) performing predetermined pairingoperations on odd-numbered ones of the input words and transmittingeven-numbered ones of the input words to the pre-common outputs; b)passing both odd- and even-numbered input data words in separate passesthrough a common processing means (CBLK) to form odd and even commonprocessing means output values, respectively; and c) in a post-commonprocessing means (POSTC), performing predetermined output scalingoperations on the odd common means output values to form post-processedodd values and arithmetically combining the post-processed odd valueswith the even common means outputs to generate high- and low-orderoutput words; the method being such that the output words containinverse discrete cosine transformation values corresponding to the inputdata words.
 2. A method according to claim 1, and comprising:a)segregating the input data words in each group into odd- and even-numbered input data words and applying the odd and even input data wordsto a pre-common processing circuit (PREC); b) directly multiplyingselected even-numbered data input words by at least one commoncoefficient; c) in the pre-common processing circuit (PREC),pre-multiplying a lowest order odd data input word by a scaling factor;d) pairwise addition of selected odd-numbered input data words to formpaired input data words; e) multiplying selected paired input data wordsby the common coefficient(s); f) pairwise grouping of intermediatecommon data words to form even and odd common output data words; g) in apost-common processing circuit (POSTC), post-multiplying by a respectiveoutput scaling coefficient each intermediate common data wordcorresponding to odd-numbered input data words; h) processing odd andeven-numbered input data words separately; and i) pairwise addition andsubtraction of even and odd output data words to form low- andhigh-order output data words.
 3. A method according to claim 1 in whichthe data input words correspond to the N² elements of an N by N block ofdigital pixel values transmitted in a frequency representation, andcomprising:a) for each of a plurality of text pixel blocks, comparingthe output data words with known target output values; b) statisticallyanalyzing the difference between actual output data words and targetoutput values; and c) forcing selected bits of selected internal datawords to predetermined binary values to minimize the expected roundingerror in arbitrary output data words.
 4. A method according to claim 1and comprising scaling all data input words by multiplying them by thesquare root of two.
 5. In combination for operating on indicationsrepresenting a discrete cosine transform to obtain indicationsrepresenting an inverse discrete cosine transform,first means forproviding the indications of the discrete cosine transform in a sequenceof input words in a block, the input words constituting even words andodd words, second means for providing common circuitry for processingthe odd words in the sequence, and for processing the even words in thesequence, to obtain indications in accordance with such processing,third means for providing circuitry prior to the common circuitry, suchprior circuitry being responsive to the indications representing thediscrete cosine transform to provide a different processing of the oddwords than the even words and to obtain indications from such priorcircuitry for introduction to the common circuitry, and fourth means forproviding post circuitry after the common circuitry, such post circuitrybeing responsive to the indications from such common circuitry forproviding arithmetic operations on particular combinations of suchindications from the even and output words to provide indicationsrelated to the inverse discrete transforms.
 6. In a combination as setforth in claim 5, the second means providing geometric and arithmeticoperations on the indications from the third means in patterns common tothe odd words and the even words in the sequence.
 7. In a combination asset forth in claim 5, the second means providing multiplication byconstant values in the geometric operations.
 8. In a combination asrecited in claim 5,the third means providing circuitry not common to theodd words and the even words, and the fourth means providing circuitrynot common to the odd words and the even words.
 9. In a combination asset forth in claim 5 the third means including fifth means for directlyintroducing the indications of the even words in the discrete cosinetransform to the second means and including sixth means for performinggeometric and arithmetic operations on the indications of the odd wordsin the discrete cosine transform to obtain the indications forintroduction to the second means.
 10. In combination for operating onindications representing a discrete cosine transform to obtainindications representing an inverse discrete cosine transform,firstmeans for providing the indications of the discrete cosine transform fora sequence of input words in a block, the input words constituting evenwords and odd words, second means for processing the indications in theeven words differently from the indications in the odd words to obtainfirst indications from the second means, third means responsive to thefirst indications from the second means for providing the sameprocessing for the output indications from the even words in the secondmeans and the output indications for the odd words from the second meansto provide second indications, and fourth means responsive to the secondindications from the third means for performing arithmetic and geometricoperations on such second indications for related pairs of odd and evenwords to obtain output indications output related to the inverteddiscrete cosine transform.
 11. In a combination as set forth in claim10, the arithmetic operations for the pair of words in the fourth meansproviding a sum of the indications in each related pair of words toprovide first output indication for one of the words in such pair andproviding a difference of the indications in the words in such relatedpair to provide a second output indication for the other word in suchpair.
 12. In a combination as set forth in claim 10, the third meansproviding geometric operations involving multiplication by particularconstants and providing arithmetic operations involving the sums of theindications in pairs of words and the differences between theindications in pairs of words.
 13. In a combination as set forth inclaim 10, the second means providing arithmetic operations involving thesums of indications in pairs of words and providing a geometricoperation involving a multiplication of the indications in another wordby a constant.
 14. In a combination as set forth in claim 10,the thirdmeans providing geometric operations involving a multiplication byparticular trigonometric constants in particular ones of the odd andeven words and providing arithmetic operations involving the sums of theindications in pairs of the odd words and corresponding pairs of theeven words and the differences between the indications in the pairs ofthe odd words and in the corresponding pairs of the even words, thesecond means providing arithmetic operations involving the sums ofindications in pairs of the odd words and providing a geometricaloperation involving a multiplication of the indications in another oneof the odd words by a constant, and the arithmetic operations for thepairs of the words in the fourth means providing a sum of theindications in each related pair of words to provide a first outputindication for one of the words in such pair and providing a differenceof the indications in the words in such related pair to provide a secondoutput indication for the other word in such pair.
 15. In a combinationas set forth in claim 10, one of the words in each pair in the fourthmeans constituting an odd word and the other one of the words in suchpair constituting an even word.
 16. In combination for operating onindications representing a discrete cosine transform to obtainindications representing an inverse discrete cosine transform,firstmeans for providing the indications of the discrete cosine transform ina sequence of input words in a block, the words constituting even wordsand odd words, second means for processing the indications of thediscrete cosine transform in the even words and in the odd words toobtain first indications, the second means including first latchingmeans for holding the first indications from the second means, means forproviding clock signals for controlling the passage of the firstindications from the second means into and out of the first latchingmeans for the second means, third means for providing the sameprocessing for the first indications from the even words in the secondmeans and the first indications from the odd words in the second meansto produce second indications from the third means, the third meansbeing operative independently of any latching means, and fourth meansfor processing the second indications and for producing thirdindications related to the inverse discrete cosine transform, the fourthmeans including second latching means responsive to the clock signalsfor controlling the times of operation of the fourth means in accordancewith the occurrence of the clock signals.
 17. In a combination as setforth in claim 16, the second means processing the indications of theeven words in the discrete cosine transform differently from theprocessing of the indications of the odd words in the discrete cosinetransform.
 18. In a combination as set forth in claim 17, the secondmeans passing to the third means the indications of the discrete cosinetransform in the even words as the first indications for such even wordsand providing arithmetic calculations of the indications of the discretecosine transform in pairs of even words to provide the first indicationsfor such even words.
 19. In a combination as set forth in claim 18, thesecond means also providing a geometric calculation on the indicationsof the discrete cosine transform in an individual one of the odd wordsand then providing the arithmetic calculations on the indications of thediscrete cosine transform in pairs of the odd words,the third meansproviding geometric calculations of the first output indications withparticular constants for particular ones of the odd words andcorresponding ones of the even words and then providing arithmeticcalculations on the first output indications for particular pairs of theodd words and corresponding pairs of the even words.
 20. In acombination as set forth in claim 19 the particular constantsconstituting trigonometric values and also the square root of two (√2).21. In a combination as set forth in claim 16 the third means processingthe first indications for the odd words differently from the firstindications for the even words.
 22. In a combination as set forth inclaim 21, the fourth means providing sums of the second indications inparticular pairs of words, one constituting and even word and the otherconstituting an odd word, and providing subtractions between theindications in the particular pairs of words.
 23. In a combination asset forth in claim 16, the third means providing geometric calculationson the first indications for particular ones of the odd words and forcorresponding ones of the even words and providing arithmeticcalculations on the first indications for particular pairs of the oddword and for corresponding pairs of the even words.
 24. In combinationfor operating on binary indications representing a discrete cosinetransform to obtain binary indications representing an inverse discretecosine transform where the binary indications representing the discretecosine transform include a binary factor representing a constant valueconstituting the square root of two (√2),first means for providing thebinary indications of the discrete cosine transform in a sequence ofinput words in a block, the input words constituting even words and oddwords, second means for processing the binary indications of thediscrete cosine transform to obtain binary output indications related tothe inverse discrete cosine transform and including the binary factorconstituting the square root of two (√2), and means for shifting thebinary output indications by one binary position to obtain a division ofthe binary output indications by a factor of two (2) and to obtainbinary indications related to the inverse discrete cosine transform. 25.In a combination as set forth in claim 24, the second means includingmeans for processing the indications in a group of words constitutingeither the odd words or the even words and for processing theindications in a group of words constituting the other of the odd wordsand the even words.
 26. In a combination as set forth in claim 24 thesecond means including precommon processing means for individuallyprocessing the binary indications representing, in the even and oddwords, the discrete cosine transform to obtain first binary indications,the precommon processing means including means for multiplying thebinary indications of the discrete cosine transform in one of the wordsby the binary factor constituting the square root of (√2),the secondmeans also including common processing means for initially processing ina particular relationship the first binary indications in a groupconstituting either the odd words or the even words and for thenprocessing in the particular relationship the first binary indicationsin a group constituting the other of the even words and the odd words,the common processing means including means for multiplying the firstbinary indications in particular ones of the odd words and correspondingones of the even words by the binary factor constituting the square rootof two.
 27. In a combination as set forth in claim 26, the commonprocessing means in the second means also including means formultiplying the first binary indications in particular ones of the oddwords and corresponding ones of the even words by binary factorsconstituting constant trigonometric values.
 28. In a combination as setforth in claim 26, the indications in the different word from the commonprocessing means having individual binary significances,the second meansincluding postcommon processing means for processing means, binaryindications form the common processing means, the postcommon processingmeans including means for processing the indications from the words ofhigher binary significance from the common processing means differentlyfrom the words of lower binary significance from the common processingmeans.